{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Project: Linear Finite Element Methods\n",
    "\n",
    " The purpose of this project is to implement the finite element method for\n",
    " solving the Poisson equation in a general polygonal domain using\n",
    " the piecewise linear finite element. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Step 1: Download and Install iFEM\n",
    "\n",
    "- Download [iFEM](https://bitbucket.org/ifem/ifem/get/tip.zip).\n",
    "- Unzip the file to where you like.\n",
    "- In MATLAB, go to the iFEM folder . \n",
    "- Run `setpath.m`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Step 2: Mesh"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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EJA0cjWhEIxqtF5A0ZDSiEY1otHZA0mDRiEY0otEmAUnDRCMa0YhGGwYkDRCNaEQjGm0e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\nBCRJUoqAJElKEZAkSSkCkiQpRf8HHp51UfAPmM0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "% Generate mesh for the unit square\n",
    "[node,elem] = squaremesh([0,1,0,1],0.25);\n",
    "showmesh(node,elem);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " - Min quality 0.7570 - Mean quality 0.9696 - Uniformity 4.34% \n"
     ]
    },
    {
     "data": {
      "image/png": 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dTnhHv9o7F07azLiPQil1Q81u3lk4/YSgbZ2N++UohH5RTBaROKHBvCAFqxvc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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "% Generate mesh for the unit disk\n",
    "[node,elem] = circlemesh(0,0,1,0.2);\n",
    "showmesh(node,elem);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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l6zbKcBDVyXHn/hNS3YDzgnuneJeaH7HGz6S8C9q+sqoWdbd7lGO52mZMjnZV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47qBibx0LiV2BXBx27Im0sVbr5W9ENT13wYtxJu99CpfcpGzoemkJQ/kfHcJXgn3UXqTEfwEn7l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\nRCAQCISJwP8HAK5SqGNtSfoAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "% Uniformly refine it to get a finer mesh\n",
    "[node,elem] = uniformrefine(node,elem);\n",
    "showmesh(node,elem);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Step 3: Assembling the matrix\n",
    "\n",
    "Compare three ways of assembling the stiffness matrix discussed in [Progamming of Finite Element Methods](http://www.math.uci.edu/~chenlong/226/Ch3FEMCode.pdf).\n",
    "\n",
    "Record the time by\n",
    "\n",
    "    tic; assemblingstandard; toc;\n",
    "    tic; assemblingsparse; toc;\n",
    "    tic; assembling; toc;\n",
    "\n",
    "Compare the computational time for different `N` by applying the uniform refinement of the initial mesh several times. Try to test the assembling until `N > 5*1e^4`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Step 4: Right hand side\n",
    "\n",
    "Using three points quadrature (i.e. 3 middle points of a triangle) to\n",
    "compute the right hand side vector."
   ]
  },
  {
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    "## Step 5: Boundary conditions\n",
    "\n",
    "* Use `findboundary.m` to get all boundary nodes and edges\n",
    "* Code pure Dirichlet boundary condition $u = g_D$\n",
    "* Code pure Neumann boundary condition $\\nabla u\\cdot n = g_N$\n",
    "* (*optional*) Code Robin boundary condition $u + d\\nabla u\\cdot n = g_R$"
   ]
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    "## Step 6: Verify convergence\n",
    "\n",
    "- Choose a smooth solution, say $u = \\sin(2\\pi x)\\cos(2\\pi y)$, calculate the right hand side $f$ and boundary conditions for the unit square. \n",
    "\n",
    "- Use your subroutine to get an approximation and use `showresult` to plot the mesh and the solution.\n",
    "\n",
    "- Use `uniformrefine` to refine the mesh and compute a sequence of solutions.\n",
    "\n",
    "- Compute the error in H1 norm and L2 norm using `getH1error` and\n",
    "`getL2error`.\n",
    "\n",
    "- Using the stiffness matrix to compute the error $\\|\\nabla(u_I - u_h)\\|$, where $u_I$ is the nodal interpolation.\n",
    "\n",
    "- Use `showrateh` to plot the rate of convergence of these error.\n",
    "\n",
    "- Test both Dirchlet and Neumann problems."
   ]
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    "## Step 7: A challenging problem\n",
    "\n",
    "Code your subroutine in a general way such that you can solve the Poisson equation on a different mesh by changing the input arguments. \n",
    "\n",
    "After you get the desireable results for the unit square, try to solve $-\\Delta u = 1$ with constant Neumann boundary conditions on the unit disk. The exact solution can be found using the polar coordinate."
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